determine whether y=1.5(1/6)^x represents exponential growth or decay
To determine whether the equation y = 1.5(1/6)^x represents exponential growth or decay, we need to explore the behavior of the equation as x increases.
Exponential growth occurs when the base of the exponential term is greater than 1. In this case, the base is (1/6), which is less than 1. Therefore, it is not exponential growth.
Exponential decay occurs when the base of the exponential term is between 0 and 1. In this case, the base is (1/6), which is between 0 and 1. Therefore, it is exponential decay.
To further understand the concept, let's analyze the equation with a few values of x:
When x = 0:
y = 1.5(1/6)^0
= 1.5 * 1
= 1.5
When x = 1:
y = 1.5(1/6)^1
= 1.5 * (1/6)
= 0.25
When x = 2:
y = 1.5(1/6)^2
= 1.5 * (1/36)
≈ 0.0417
As x increases, the value of y decreases progressively. This confirms that the equation represents exponential decay.